[tex]7^{\dfrac{lg(lg5)}{lg7}} = 7^{\dfrac{lg(lg5)}{log_\big{10}7}} =7^{\dfrac{lg(lg5)}{\dfrac{1}{log_{7}{10}}}}= 7^{\Big{lg(lg5)\cdot \dfrac{log_\big{7}10}{1}}} = \\ \\ =7^{\Big{lg(lg5)\cdot log_\big{7}10}} = {\Big(7^{\big{log_\big710}}\Big)}^{\big{lg(lg5)}} = 10^{\big{lg(lg5)}} = 10^{\big{log_\big{10}lg5}} = \\ \\ = lg5[/tex]
[tex]\\ $M-am folosit de proprietatile: \left\| \begin{array}{c} log_\big{a}b = \dfrac{1}{log_\big{b}a} \\ a^{\Big{log_\big{a}b}} = b\end{array} \right |[/tex]
